In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which is obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given. E-mail: [email protected] New E-mail address: [email protected]

Hopf algebra structure on the differential algebra of the extended q-plane is defined. An algebra of forms which is obtained from the generators of the extended q-plane is introduced and its Hopf algebra structure is given. E-mail: [email protected] E-mail: [email protected]

In this paper, we study the integration of functional logic programming and databases by presenting a data model, and a query and data definition language. The query and data definition language is based on the use of a set of algebra operators over an extended relational algebra. The algebra expressions built from the extended algebra are used for expressing queries and rules. In addition, alg...

This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every $L$-Lipschitz graph over a subset $k$-dimensional horizontal subgroup $\mathbb{V}$ $\mathbb{H}^n$ can be extended to an $L'$-Lipschitz entire $\mathbb{V}$, where $L'$ depends only on $L$,...

in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

We show that the representation theory for the toroidal extended affine Lie algebra is controlled by a VOA which is a tensor product of four VOAs: a sub-VOA V + Hyp of a hyperbolic lattice VOA, affine ˙ g and sl N VOAs and a Virasoro VOA. A tensor product of irre-ducible modules for these VOAs admits the structure of an irreducible module for the toroidal extended affine Lie algebra. We also sh...

Note that the above does not require independence. To prove Theorem 1, it therefore suffices to bound ∑n i=1 α 2 i . Kontorovich & Ramanan (2008, Remark 2.1) showed that, if f is c-Lipschitz with respect to the Hamming metric, then ∑n i=1 α 2 i ≤ nc ‖Θ π n‖ 2 ∞. (Though the published results only prove this for countable spaces, Kontorovich later extended this analysis to continuous spaces in h...